Asst 14 Query

course Phy 201

㸯x~ˇassignment #014

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014. `query 14

Physics I

03-03-2007

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18:37:00

set 3 intro prob sets

If you calculate the acceleration on a mass m which starts from rest under the influence of a constant net force Fnet and multiply by a time interval `dt what do you get?

How far does the object travel during this time and what velocity does it attain?

What do you get when you multiply the net force by the distance traveled?

What kinetic energy does the object attain?

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RESPONSE -->

F/m = a

a * `dt = `dv

`ds = `dt * `dv

`ds = `dt * vAve, not `dt * `dv

vf = sqrt (v0^2 + 2as)

Fnet * `ds = `dWnet

KE = `dWnet

`dKE = `dWnet

KEf = KE0 + `dKE.

In this situation the object starts from rest so KE0 = 0, and it's correct to say that KEf = `dWnet.

.

confidence assessment: 2

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18:39:37

**STUDENT ANSWER AND INSTRUCTOR COMMENTS: a*'dt = the final velocity if V0=0. to get the change in position you would divide the final velocity(since V0=0) by 2 to get the average velocity and then multiply that by the 'dt to get the units of distance traveled.

Multiply that by the 'dt to get the units of distance traveled. It attains a Vf of a*'dt as shown above because V0=0, if V0 was not zero you would have to add that to the a*'dt to get the final velocity.

When you multiply Fnet by 'dt you get the same thing you would get if you multiply the mass by the change in velocity(which in this case is the same as the final velocity). This is the change in momentum. The Kinetic Energy Attained is the forcenet multiplied by the change in time.

a = Fnet / m. So a `dt = Fnet / m * `dt = vf.

The object travels distance `ds = v0 `dt + .5 a `dt^2 = .5 Fnet / m * `dt^2.

When we multiply Fnet * `ds you get Fnet * ( .5 Fnet / m * `dt^2) = .5 Fnet^2 `dt^2 / m.

The KE attained is .5 m vf^2 = .5 m * ( Fnet / m * `dt)^2 = .5 Fnet^2 / m * `dt^2.

Fnet * `ds is equal to the KE attained.

The expression for the average velocity would be [ (v0 + a * `dt) + v0 ] / 2 = v0 + 1/2 a `dt so the displacement would be (v0 + 1/2 a `dt) * `dt = v0 `dt + 1/2 a `dt^2. This is equal to (v0 `dt + 1/2 a `dt^2) * Fnet = (v0 `dt + 1/2 a `dt^2) * m a , since Fnet = m a. **

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RESPONSE -->

Is what I said right as well?

self critique assessment: 2

The solution should be expressed in terms of the 'given' quantities Fnet, m and `dt.

Except for your `ds = `dt * `dv error, your reasoning provided a correct pathway to the solution. It would have led to the correct result if you had substituted the expressions you got earlier into your final expression.

You should be able to reconcile your process with the final expression .5 Fnet^2 `dt^2 / m. Let me know if you can't.

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18:54:50

Define the relationship between the work done by a system against nonconservative forces, the work done against conservative forces and the change in the KE of the system. How does PE come into this relationship?

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RESPONSE -->

KE = Wnet done on a system. Positive work done by a system against nonconservative and/or conservative forces decreases KE. Negative work done by a system on conservative and/or nonconservative forces increases KE. Positive work done against conservative forces = `dPE. Generally, PE decreases as KE increases.

confidence assessment: 2

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18:58:56

** The work done by the system against all forces will decrease the KE by an equal amount. If some of the forces are conservative, then work done against them increases the PE and if PE later decreases this work will be recovered. Work done against non-conservative forces is not stored and cannot be recovered.

STUDENT RESPONSE WITH INSTRUCTOR COMMENTARY: The work done by a system against nonconservative forces is the work done to overcome friction in a system- which means energy is dissipated in the form of thermal energy into the 'atmosphere.'

Good. Friction is a nonconservative force.

However there are other nonconservative forces--e.g., you could be exerting a force on the system using your muscles, and that force could be helping or hindering the system. A rocket engine would also be exerting a nonconservative force, as would just about any engine. These forces would be nonconservative since once the work is done it can't be recovered.

STUDENT RESPONSE WITH INSTRUCTOR COMMENTS: The work done by a system against conservative forces is like the work to overcome the mass being pulled by gravity.

INSTRUCTOR COMMENT: not bad; more generally work done against conservative force is work that is conserved and can later be recovered in the form of mechanical energy **

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RESPONSE -->

I shouldn't have said that negative work done by a system on nonconservative forces increases KE.

What would be an example of negative work done by a system against nonconservative forces? Does that affect KE at all?

self critique assessment: 2

An elastic force is conservative (think of an ideal rubber band that doesn't dissipate any of its energy in the form of thermal energy, etc.; an object bouncing up and down on such a rubber band could continue bouncing indefinitely with no additional input of energy).

Assuming that the net force on the object is the force exerted by the rubber band (i.e., that no other forces are acting):

When the rubber band is pulling the object in the direction of motion, the object speeds up.

When the rubber band is pulling the object in the direction of motion, the object exerts an equal and opposite force against the conservative force so the object does negative work against the conservative force.

When the rubber band is pulling the object in the direction of motion, the conservative force does positive work on it.

When the rubber band is pulling the object in the direction of motion, it does negative work against the conservative force.

The work done by the conservative force on the object is equal and opposite to the work done by the object against the conservative force.

Similar statements could be made about a gravitational force. An object in the gravitational field of the Earth exerts a force on the Earth which is equal and opposite to the gravitational force exerted by the Earth on it. Within that field, near the surface of the Earth:

The force exerted by the Earth's gravity on a mass is in the direction we regard as downward.

The gravitational force exerted by the mass on the Earth is upward. This upward force can also be regarded as the force exerted by the object against the Earth's gravitational field.

The force exerted by the mass against the gravitational field of the Earth is upward.

If an object moves upward the gravitational field of the Earth does negative work on it (force and displacement are in opposite direction).

An object which moves 'upward' does positive work against gravity.

An object which moves 'upward' under only the gravitational force slows down, loses KE.

An object which moves 'downward' under only the gravitational force speeds up, gains KE.

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20:05:36

class notes: rubber band and rail

How does the work done to stretch the rubber band compare to the work done by the rubber band on the rail, and how does the latter compare to the work done by the rail against friction from release of the rubber band to the rail coming to rest?

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RESPONSE -->

The work done to stretch the rubber band is W = Fnet * `ds. The Fnet is composed of conservative force to pull the rubber band and negative force of friction. This work is equal to the work done by the rubberband on the rail. The work done by the rail against friction is also equal to this work.

confidence assessment: 0

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20:06:32

** The work done to stretch the rubber band would in an ideal situation be available when the rubber band is released.

Assuming that the only forces acting on the rail are friction and the force exerted by the rubber band, the work done by the rail against friction, up through the instant the rail stops, will equal the work done by the rubber band on the rail.

Note that in reality there is some heating and cooling of the rubber band, so some of the energy gets lost and the rubber band ends up doing less work on the rail than the work required to stretch it. **

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RESPONSE -->

so the work done should be nearly equal between all three, correct?

self critique assessment: 3

Clarification:

The work done by the rubber band on the rail is taken to be the work done by the rubber band after release. This is implicit in the context, but it wouldn't have been a bad idea for me to state it explicitly.

For an 'ideal' rubber band the three would in fact be equal. For a real rubber band, the energy required to stretch is less than the work it does in the rebound, but the situation is complicated by the fact that the rubber band heats up and cools down in complex and perhaps counterintuitive ways.

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20:13:33

Why should the distance traveled by the rail be proportional to the F * `ds total for the rubber band?

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RESPONSE -->

Because the same amount of work that is done on the rubberband will then be transferred to the rail since the same forces apply.

confidence assessment: 1

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20:13:59

** The F `ds total of the rail when it is accelerated by the rubber band is equal Fave `ds, which is equal to to m * aAve * `ds. Here aAve is the average acceleration of the rail by the rubber band.

2 aAve `ds = vf^2 - v0^2 by the fourth equation of motion. So the F `ds total is proportional to the change in v^2.

The rail is then stopped by the frictional force f; since f `ds is equal to m * a * `ds, where a is the acceleration of the sliding rail, it follows that f `ds is also proportional to the change in v^2.

Change in v^2 under the influence of the rubber band (rest to max vel) is equal and opposite to the change in v^2 while sliding against friction (max vel back to rest), so work f `ds done by friction must be equal and opposite to F `ds.

This ignores the small work done by friction while the rubber band is accelerating the rail. **

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RESPONSE -->

ok

self critique assessment: 3

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20:45:10

gen phy A person of mass 66 kg crouches then jumps to a height of .8 meters. From the crouches position to the point where the person leaves the ground the distance is 20 cm. What average force is exerted over this 20-cm distance?

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RESPONSE -->

Fgrav = 6.6 kg * -9.8 m/s/s = -65 N

Force exerted = 65 N

confidence assessment: 0

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21:03:25

** the normal force is the force between and perpendicular to the two surfaces in contact, which would be 646.8N if the jumper was in equilibrium. However during the jump this is not the case, and the normal force must be part of a net force that accelerates the jumper upward.

In a nutshell the net force must do enough work to raise the person's weight 1 meter while acting through only a .2 meter displacement, and must therefore be 5 times the person's weight. The person still has to support his weight so the normal force must be 6 times the person's weight.

The detailed reasoning is as follows:

To solve this problem you have to see that the average net force on the jumper while moving through the `dy = 20 cm vertical displacement is equal to the sum of the (upward) average normal force and the (downward) gravitational force:

Fnet = Fnormal - m g.

This net force does work sufficient to increase the jumper's potential energy as he or she rises 1 meter (from the .20 m crouch to the .8 m height). So

Fnet * `dy = PE increase,

giving us

( Fnormal - m g ) * `dy = PE increase.

PE increase is 66 kg * 9.8 m/s^2 * 1 meter = 650 Joules approx.

m g = 66 kg * 9.8 m/s^2 = 650 Newtons, approx..

As noted before `dy = 20 cm = .2 meters.

So

(Fnormal - 650 N) * .2 meters = 650 Joules

Fnormal - 650 N = 650 J / (.2 m)

Fnormal = 650 J / (.2 m) + 650 N = 3250 N + 650 N = 3900 N.

An average force of 3900 N is required to make this jump from the given crouch.

This is equivalent to the force exerted by a 250-lb weightlifter doing a 'squat' exercise with about 600 pounds on his shoulders. It is extremely unlikely that anyone could exert this much force without the additional weight.

A 20-cm crouch is only about 8 inches and vertical jumps are typically done with considerably more crouch than this. With a 40-cm crouch such a jump would require only half this total force and is probably feasible. **

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RESPONSE -->

I don't understand where the concept of Fnormal came from or what it means.

This is what I should have done:

Fnet * `dy = PE increase

(Fnormal - m*g) * 20 cm = 66 * 9.8 m/s/s * 1 m

(Fnormal - 650 N ) * .2 M = 650 J

Divide by .2 m

Fnormal - 650 N = 3250 N

add 650 N

Fnormal = 3900 N

I really don't understand where most of this came from.

self critique assessment: 2

Quoting from the given solution

'the normal force is the force between and perpendicular to the two surfaces in contact'

The two surfaces in contact are the bottom of the player's shoes and the floor.

In equilibrium the net force on the player is zero, so the normal force must be equal and opposite to the gravitational force exerted on him by the surface of the Earth.

In equilibrium the player would have 0 acceleration and would never attain any vertical velocity relative to the floor, so he would never move up off the floor. The normal force is the only force other than gravity acting on the player. So the normal force must have a magnitude greater than the gravitational force.

To increase PE by 650 J (this is the PE change from the start of the jump to the high point), the net force must do 650 J of work against gravity. This is energy conservation.

The net force is the resultant of the two forces acting on the player, which are Fnormal and weight. These forces act in opposite directions. If upward is positive then the net force is Fnormal - weight.

Even after considering these statements you might well have questions. You're doing well but it still takes some thinking to reconcile these ideas. I'll be glad to answer additional questions.

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21:03:51

univ phy text prob 4.42 (4.40 in 10th edition) Mercury lander near surface upward thrust 25 kN slows at rate 1.2 m/s^2; 10 kN speeds up at .8 m/s^2; what is weight at surface?

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RESPONSE -->

i'm in phy 201

confidence assessment: 3

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21:03:56

** If a landing craft slows then its acceleration is in the direction opposite to its motion, therefore upward.

If it speeds up while landing that its acceleration is in the direction of its motion, therefore downward.

If the upward motion is taken as the positive direction, then the acceleration under a thrust of 25 kN is + 1.2 m/s^2, and the acceleration when under thrust of 10 kN is - .8 m/s^2.

In either case m * a = net force.

Net force is thrust force + gravitational force.

1 st case, net force is 25 kN so m * 1.2 m/s/s + m * g = 25 kN.

1 st case, net force is 10 kN so m * (-.8 m/s/s ) + m * g = 10 kN.

Solve these equations simultaneously to get the weight m * g (multiply 1 st eqn by 2 and 2d by 3 and add equations to eliminate the first term on the left-hand side of each equation; solve for m * g).

The solution is m * g = 16,000 kN.

Another solution:

In both cases F / a = m so if upward is positive and weight is wt we have

(25 kN - wt) / (1.2 m/s^2) = m and

(10 kN - wt) / (-.8 m/s^2) = m so

(25 kN - wt) / (1.2 m/s^2) = (10 kN - wt) / (-.8 m/s^2).

Solving for wt we get 16 kN. **

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RESPONSE -->

ok

self critique assessment: 3

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"

See my notes and let me know if you have additional questions. You're doing well.